Ultra-low power and ultra-low voltage bandgap voltage regulator device and method thereof

ABSTRACT

A family of bandgap embodiments are disclosed herein, capable of operating with very low currents and low power supply voltages, using neither any custom devices nor any special manufacturing technology, and fabricated on mainstream standard digital CMOS processes. As such, manufacturing cost can be kept low, manufacturing yields of digital CMOS system-on-a-chip (SOC) that require a reference can be kept optimal, and manufacturing risk can be minimized due to its flexibility with respect to fabrication process node-portability. Although the embodiments disclosed herein use novel techniques to achieve accurate operations with low power and low voltage, this family of bandgaps also uses parasitic bipolar junction transistors (BJT) available in low cost digital CMOS process to generate proportional and complementary to absolute temperature (PTAT and CTAT) voltages via the base-emitter voltage (V EB ) of BJTs and scaling V EB  differential pairs to generate the BJTs thermal voltage (V T ).

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

The present invention claims priority from U.S. Provisional Patent Application Ser. No. 61/756,490, filed Jan. 25, 2013 and U.S. Provisional Patent Application Ser. No. 61/865,559 filed Aug. 13, 2013, both disclosures of which are herein specifically incorporated by reference in their entirety.

FIELD OF THE INVENTION

This invention relates to improvements in voltage regulators for integrated circuits.

BACKGROUND

Voltage regulators are fundamental functions in powering most analog or digital functions in electronic systems. Operating at low currents, low power supply voltages, and over extended temperatures are key objectives in portable electronics systems, including in system-on-chips (SOC), especially in medical or emerging wireless and battery-less applications such as power-on-a-chip (PoC), Internet-of-things (loT), or energy harvesting, to name a few.

In light of the potentially large markets for such emerging applications, unless solution costs are low, the markets may not realize their full potential reach. As such, low cost innovations in component designs are needed to enable such prospects of high volume markets to get off the ground and take off. In the last few decades, there has been a tremendous amount of annual manufacturing investment in semiconductors, some of which is sunk-cost. As a result, there is likely ample capacity in standard complementary metal-oxide-semiconductor (CMOS) manufacturing factories that may be readily and cheaply available for exploitation by new and promising high volume markets. The enablement of such new high volume markets would greatly benefit if their solutions require neither any custom devices nor any special processes, which could impose higher costs or risks on manufacturing yields. For design solutions in such emerging applications, to optimally exploit the existing digital CMOS capacity, manufacturing process node-portability should not be impeded. While the die-size of such solutions need to be kept small to keep the costs down, optimally no performance interference on the rest of the functions of the SOC should be imposed by innovative designs when serving such new applications requirements (low voltage and ultra-low current over maximal power supply and temperature spans).

A survey of alternative voltage regulator topologies is presented in Fayomi, C J B. et al (2010) “Sub 1 V CMOS bandgap reference design techniques: a survey”, AICSP 62:141-157, DOI 10.1007/s10470-009-9352-4 discusses many techniques and their trade-offs for low power references and which is hereby incorporated by reference. Some of the trade-offs which are discussed in Fayomi et al. are briefly summarized as follows. Using Bipolar CMOS (BiCMOS) processes or depletion mode CMOS transistors frees up some operational supply headroom but adds to fabrication complexity and cost. Also, utilizing process deviations such as threshold differentials between positive channel metal-oxide semiconductors (PMOS) and negative channel metal-oxide semiconductors (NMOS), multiple depletion mode transistors, and differential thresholds via channel length variations. Alternatively, using custom devices such as a dynamic threshold metal-oxide semiconductor transistor (DTMOST), bulk driven CMOS, or lateral positive negative positive transistors (PNPs) can provide some design flexibility in extending digital power supply voltage (V_(DD)) and bandgap voltage (V_(BG)) spans, but at a price. Such deviations impose additional manufacturing costs, require special device modeling, or may demand post production control monitoring for the entire SOC that contains the reference. There are other design techniques, such as switch capacitors, that can provide extra operational headroom without the need for process or device variations. Switching techniques can help make low-noise references with stable temperature coefficients (TC) but may add cost due to capacitor extra mask or large capacitors for low droop rates. Chopping bandgap topologies can also cause high transient current consumption or may interfere with other substrate-noise sensitive analog functions within the SOC. Moreover, switch capacitor topologies can increase latch up risk and may require on chip charge-pumps in sub-1V environments. Banking only on CMOS transistors in subthreshold (which emulate pseudo-bipolar junction transistor (BJT) like behavior) to generate a V_(BG) helps with low-power and sub-1V objectives, but such designs generally exhibit wider V_(BG) variations, and likely require extra trimming and testing cost in post production. Forward biasing PMOS or NMOS body-source terminals can help increase bandgap amplifier headroom, but requires proper modeling at different process nodes. Additionally, such a design approach generally entails increased parasitic current and leakage risk at elevated temperatures, which limits the reference high temperature operations. The majority of reference topologies that impose on the SOC by requiring special processes or rely on non-standard use of transistors have not made it to high-volume applications. This is not just because of their added manufacturing cost, special device characterization, or special device modeling requirements. As noted earlier, variations on process, and deviation on devices for one function of an SOC (such as a reference) increases costs and manufacturing risk on the entire SOC and handicaps the SOC's process node portability, which ties the manufacturer's hands.

SUMMARY OF THE INVENTION

An aspect of the disclosure herein is a fractional bandgap reference circuit comprising: a voltage loop having two scaled transistors to provide a positive TC signal across a first resistor; a feedback loop having a first amplifier which generates a positive TC signal across a second resistor and a third resistor; a second amplifier controlling a plurality of current sources which conjunctively produce the residual signal with near zero TC to the feedback loop to produce a voltage reference across a fourth resistor; and wherein the voltage loop positive TC signal is supplied by the positive TC signal of the feedback loop to generate the residual signal with near zero TC.

Another aspect of the disclosure herein is a method of creating a fractional bandgap comprising: providing a positive TC signal across a first resistor from a voltage loop having two scaled transistors; generating a positive TC signal from a feedback loop having a first amplifier across a second resistor and a third resistor; controlling a plurality of current sources by a second amplifer to conjunctively produce a residual signal with near zero TC to the feedback loop to produce a voltage reference across a fourth resistor; and generating the residual signal with near zero TC by supplying the voltage loop positive TC signal from the positive TC signal of the feedback loop.

Another aspect of the disclosure herein is a fractional bandgap reference circuit comprising: a voltage loop having a first transistor and second transistor isolated by a first amplifier from a first resistor and which creates a positive TC current and a negative TC voltage; a second amplifier in conjunction with a plurality of current sources to receive the positive TC current from the voltage loop and supply a feedback loop with a positive TC signal; and the feedback loop having a scaled second resistor and third resistor which receive the positive TC current, which is fed to a second and a third resistors to produce a positive TC voltage that is combined with the negative TC voltage to generate a near zero TC voltage as a reference voltage.

Another aspect of the disclosure herein is a method of generating a fractional bandgap comprising: isolating a voltage loop having a first transistor and second transistor by a first amplifier from a first resistor, wherein the voltage loop creates a positive TC current and a negative TC voltage; receiving the positive TC current at an amplifier and conjunctively with a plurality of current sources to supply feedback loop with a positive TC signal; and receiving the positive TC signal at the feedback loop which includes a scaled second resistor and third resistor and which feeds a positive TC current to a second resistor and a third resistor to produce a positive TC voltage that is combined with the negative TC voltage to generate a near zero TC voltage as a reference voltage.

Another aspect of the disclosure herein is a fractional bandgap reference circuit comprising: a voltage loop having a first transistor, a second transistor, first amplifier and a first resistor; said first resistor connected to the base of the first transistor to isolate a quiescent current of the first transistor from the current through the first transistor to generate a positive TC current; and said first amplifier buffering a negative TC voltage between the voltage loop and a feedback loop; a second amplifier in conjunction with a plurality of current sources which receives a positive TC current that was generated by the voltage loop and supplies feedback loop with a positive TC signal; and the feedback loop having a scaled second resistor and third resistor which receive the positive TC current, which is fed into the second and the third resistors to generate a positive TC voltages that is combined with the negative TC voltage to generate a near zero TC voltage as a reference voltage.

Another aspect of the disclosure herein is a bandgap reference circuit comprising: a plurality of V_(T) cells connected in series to produce a V_(PTAT); wherein each of said V_(T) cells comprise a first amplifier and scaled first transistor and second transistor operating at scaled currents which are biased by the two scaled current sources; said first amplifier generating a positive TC output voltage at a base of the first transistor so that the amplifier inputs are substantially equalized; a V_(EB) transistor biased by a current source to generate a V_(CTAT); and wherein the V_(PTAT) and V_(CTAT) are connected in series to create a voltage reference.

Another aspect of the disclosure herein is a method of producing a bandgap reference comprising: producing a V_(PTAT) from a plurality of V_(T) cells connected in series; wherein each of said V_(T) cells comprise a first amplifier and scaled first transistor and second transistor operating at scaled currents which are biased by at least two scaled V_(T) cell current sources; said first amplifier generating a positive TC output voltage at a base of the first transistor so that the amplifier inputs are substantially equalized; biasing a V_(EB) transistor by a current source to generate a V_(CTAT); and creating a voltage reference from the V_(PTAT) and the V_(PTAT).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic circuit diagram of a first embodiment illustrating a bandgap (or fractional bandgap) in a voltage regulator circuit.

FIG. 2 is a schematic circuit diagram of second embodiment illustrating a bandgap (or fractional bandgap) in a voltage regulator circuit.

FIG. 3 is a schematic circuit diagram showing a third embodiment of an alternative bandgap reference to FIG. 2.

FIG. 4 is a schematic circuit diagram showing a bandgap reference according to a fourth embodiment.

FIG. 5 is a circuit schematic showing a prior art conventional bandgap reference.

DETAILED DESCRIPTION

Numerous embodiments are described in the present application and are presented for illustrative purposes only. The described embodiments are not, and are not intended to be, limiting in any sense. One of ordinary skill in the art will recognize that the disclosed embodiment(s) may be practiced with various modifications and alterations, such as structural, logical, and electrical modifications. Although particular features of the disclosed embodiments may be described with reference to one or more particular embodiments and/or drawings, it should be understood that such features are not limited to usage in the one or more particular embodiments or drawings with reference to which they are described, unless expressly specified otherwise.

The present disclosure is not a literal description of all embodiments of the invention(s). Also, the present disclosure is not a listing of features which must necessarily be present in all embodiments On the contrary, a variety of components are described to illustrate the wide variety of possible embodiments of the present invention(s).

Although process (or method) steps may be described or claimed in a particular sequential order, such processes may be configured to work in different orders. In other words, any sequence or order of steps that may be explicitly described or claimed does not necessarily indicate a requirement that the steps be performed in that order. The steps of processes described herein may be performed in any order possible. Further, some steps may be performed simultaneously despite being described or implied as occurring non-simultaneously (e.g., because one step is described after the other step). Moreover, the illustration of a process by its depiction in a drawing does not imply that the illustrated process is exclusive of other variations and modifications thereto, does not imply that the illustrated process or any of its steps are necessary to the embodiment(s), and does not imply that the illustrated process is preferred.

Although a process may be described as including a plurality of steps, that does not imply that all or any of the steps are preferred, essential or required. Various other embodiments within the scope of the described invention(s) include other processes that omit some or all of the described steps.

Although a circuit may be described as including a plurality of components, aspects, steps, qualities, characteristics and/or features, that does not indicate that any or all of the plurality are preferred, essential or required. Various other embodiments may include other circuit elements or limitations that omit some or all of the described plurality.

The following description has been presented for purposes of illustration and description and is not intended to be exhaustive or to limit the embodiments to the precise form disclosed. Many modifications and variations are possible in light of the teachings disclosed herein. The embodiments were chosen and described to explain principles of operation and their practical applications. However, the scope of the invention is to be defined by the claims.

As mentioned earlier, over the last few decades, multi-billion dollar annual investments in equipment and fabrication technologies have resulted in advancements in low voltage sub-micron CMOS processes that have yielded continued improvements in die density, tightly controlled device parameters {i.e. threshold voltage (V_(TH)), Boltzmann Constant (k), oxide thickness (T_(ox)), and other parameters}, and increased matching. Naturally, such manufacturing advancements have materially helped enhance the performance, precision, and matching of analog functions (i.e., conventional 2-stage amplifiers with lower offset, lower offset drift, and tighter matching) which is leveraged in the disclosure herein. The embodiments described in this application may be implemented using standard digital CMOS processes and parasitic vertical BJTs with inherent predictability due to the stable device physics base-emitter voltage (V_(BE)) and V_(T) parameters that should enhance manufacturing viability and ease design portability. The majority of transistors used in the bandgap family operate in the sub-threshold region to accommodate their low power objective and help with headroom without use of any custom devices. Additional analysis of relevant to low power and low cost bandgap designs are also hereby incorporated by reference: 1) Ali Far, (2013), “A 5 μW Fractional CMOS Bandgap Voltage and Current Reference”, 2013 IEEE GHTCE Conference Proceedings, China; 2) Ali Far, (2013), “A 400 nW CMOS Bandgap Voltage Reference”, 2013 IEEE ICEESE Conference Proceedings, Malaysia.; and 3) Ali Far, (2014), “A Low Supply Voltage 2 μW Half Bandgap Reference In Standard Sub-μ CMOS”, 2014 IEEE CONNECT Conference Proceedings, India.

The term “near zero” is used throughout this disclosure and hereby a brief explanation is provided as follows. A bandgap voltage, or a fractional bandgap voltage, generally is a voltage that has near zero temperature coefficient (TC). For example for a bandgap reference to have a near zero TC, the output reference voltage can be about 1.2V with variations for instance in the range of +/−10 mV over a span of temperature from negative 50 degrees centigrade to positive 150 degrees centigrade (i.e. 1.99V<VBG<1.21V with −50 C<T<+150 C). Bandgaps without (post manufacturing adjustments or) trim can have wider variations such as for example +/−50 mV or tighter variations of for example +/−1 mV with trim. For a fractional bandgap (say for a half bandgap), an example of near zero TC half bandgap reference voltage could be about 0.6V with variations for instance in the range of +/−5 mV over a span of temperature from negative 50 degrees centigrade to positive 150 degrees centigrade (i.e. 0.595V<VHBG<6.05V with −50 C<T<+150 C). Half bandgaps without (post manufacturing adjustments or) trim can have wider variations such as for example −/−25 mV or tighter variations of for example +/−0.5 mV with trim.

In the first embodiment discussed herein a bandgap voltage V_(BG) may be generated by adding (or combining) a proportional to absolute temperature (PTAT) voltage, V_(PTAT), whose voltage increases with temperature (positive TC) to a complementary to absolute temperature (CTAT) voltage, V_(CTAT), whose voltage decrease with temperature (negative TC). Henceforth, summation of the V_(CTAT) (with a negative TC) and V_(PTAT) (with a positive TC) can be scaled via resistors (i.e. resistor dividers) to produce a fractional bandgap voltage, V_(ra), which is substantially constant over temperature variation. This fractional bandgap reference embodiment may be implemented using standard CMOS manufacturing processes, and may not require any custom device or special process, and hence has lower production costs. One of the benefits of these embodiments is that both a fractional current reference I_(ra) and a fractional voltage reference V_(ra) are generated concurrently and low current consumption is optimized around ambient temperature (which is where some applications operate most of the time). This first embodiment includes elements such as amplifiers, resistors, BJTs, and CMOS transistors (i.e. PMOS transistors that can be configured to function as current sources).

FIG. 1 is a circuit schematic showing a bandgap reference according to the first embodiment. Throughout this description the values of R_(f1a)=R_(f2a)=R_(fa) and current source values which are determined as a function of PMOS W/L scale factors may be set to a predetermined value b=c=d=1. Also note that ‘b’, ‘c’, and ‘d’ scale factors may each be in a predetermined range of 1 to 10 depending on considerations such as die size and current consumption amongst others. The current through R_(ia) is a PTAT current where I_(Ria) has a positive TC, comprised of the difference of V_(EB) voltages (between Q_(1a) and Q_(2a)) across R_(ia). One terminal of each of R_(f1a) and R_(f2a) is connected to the reference output V_(ra), with near zero TC, while each of R_(f1a) and R_(f2a)'s other terminal is connected to a V_(EB) (of Q_(ia) and Q_(2a)) potential with a negative TC. As a result, R_(fa)'s current I_(Rfa) will increase with temperature. Now I_(Ria)+I_(Rfa)+I_(ra)≈0 in order to meet the requirement that sum of currents at a circuit node must be zero. Since I_(D) of P_(3a)=V_(ra)/R_(Oa)=I_(ra), then the I_(D) in P_(ia) through P_(4a) is equal to I_(ra). Moreover, since I_(Ria) increases with temperature and I_(Rfa) supplies R_(ia) with the positive TC current it needs, then the residual I_(ra) is left for the current sources that would be biased with a near zero TC. Therefore, P_(1a) through P_(4a) operate at an I_(D) that has constant TC that is I_(ra), which generates the fractional voltage reference across R_(oa) before it is buffered to generate V_(ra).

The connections of the elements in FIG. 1 are described as follows.

Transistors P_(1a), P_(2a), P_(3a), and P_(4a) have their source terminals connection to node 1 which is the positive supply voltage or V_(DD). Also, P_(1a) through P_(4a) have their gates connected to node 6 a, whose voltage is driven by the output node of amplifier A_(1a). At node 3 a, drain of P_(1a) is connected to the emitter of BJT, Q_(1a), as well as the inverting input terminal of amplifier A_(1a). At node 2 a, emitter of BJT, Q_(2a), is connected to one terminal of R_(ia). At node 4 a, drain of P_(2a) is connected to the other terminal of resistor R_(ia) as well as non-inverting input terminal of A_(1a). Collectors and bases of Q_(1a) and Q_(2a) are connected to V_(SS), which is node 0. At node 7 a, drain of P_(3a) is connected to one terminal of resistor R_(Oa) whose other terminal is connected to the ground potential. Also, node 7 a is where the fractional bandgap voltage is generated. At node 5 a, the inverting input of A_(2a) is connected to its output, which configures A_(2a) as a unity gain amplifier buffer, enabling node 5 a which is V_(ra) to substantially equal the voltage at node 7 a. Also, the buffered V_(ra) voltage at node 5 a is able to drive the common terminal of R_(f1a) and R_(f2a) feedback resistors, whose other terminals are connected to nodes 3 a and 4 a respectively. Setting the source voltages of transistors P_(1a) through P_(4a) to the same voltage at node 1 and setting their gates to the same voltage at node 6 a enables configuring transistors P_(1a) through P_(4a) as four current sources whose quiescent currents can be scaled substantially proportional to their respective transistors' width over length ratios, W/L. Node 8 a is the drain of PMOS transistor P_(4a) which operates and provides a reference current source. For example, in the FIG. 1 circuit schematic (W/L)_(P1a)=b×(W/L)_(P2a), and (W/L)_(P3a)=c×(W/L)_(P2a), and (W/L)_(P4a)=d×(W/L)_(P2a), which accommodates scaling PMOS current sources P_(1a), P_(3a), and P_(4a) quiescent currents may be substantially scaled as multiples of ‘b’, ‘c’, and ‘d’ times the quiescent current in P_(2a). In the embodiment described here, b=c=d=1, which causes the quiescent currents in P_(1a) through P_(4a) to be equal (or substantially equal) and the same (or approximately the same) as I_(ra). Also note that ‘b’, ‘c’, and ‘d’ scale factors may each be in a predetermined range of 1 to 10 depending on considerations such as die size and current consumption, amongst others.

The details of various functions of the circuit in FIG. 1 are described in 2 segments.

In the first segment, we begin with the voltage loop that starts (at node 0) going through V_(BE) of Q_(2a) (to node 2 a) then through R_(ia) (to node 4 a) then across A_(1a) inputs (to node 3 a) and finally back through V_(EB) of Q_(2a) to node zero (0). In describing the operation of this voltage loop, amplifiers A_(1a) and A_(2a) have substantially minimal offset voltages. Also, note that V_(EB) of Q is denoted as V_(EB)|_(Q) and I_(D) of P is denoted as I_(D)| P. V _(EB)|_(Q1a) ≈I _(Ria) ×R _(ia) +V _(EB)|_(Q2a). Thus: V _(EB)|_(Q1a) −V _(EB)|_(Q2a) ≈I _(Ria) ×R _(ia) ≈ΔV _(EB). Therefore, I _(Ria) ≈ΔVEB/R _(ia)≈(V _(EB)|_(Q1a) −V _(EB)|_(Q2a))/R _(ia). To generate ΔV_(EB), the emitter areas of Q_(2a) are scaled ‘a’ times bigger than that of Q_(1a), and as described earlier the quiescent currents for Q_(1a) and Q_(2a) can be scaled via P_(2a) and P_(1a) currents, whose W/Ls are scaled by ‘b’: ΔV _(EB) ≈V _(EB)|_(Q1a) −V _(EB)|_(Q2a) ≈V _(T)×ln(a×b), where V_(T) is the thermal voltage and equal to (K×T)/q and k is the Boltzmann constant, q is the electron charge, and T is the temperature. Thus: I _(Ria) ≈I _(PTAT) ≈ΔV _(EB) /R _(ia) ≈V _(T).×ln(a×b)/R _(ia). Note for example that for a=5 and b=11, then 100 mV≈VT×ln(55) could be a typical value of V_(T)×ln(a×b) term in the above equation. Consistent with principles of conventional bandgaps (such as the ones depicted in prior art FIG. 5), note that ΔV_(EB) tracks V_(T) which has a positive TC, and this yields the PTAT signal (current) needed in the bandgap.

In the second segment, we turn our attention to the mechanism by which fractional reference current I_(ra) and voltage V_(ra) (with near zero temperature variations) are generated conjunctively. As noted earlier, in this embodiment: b=c=d=1 I _(D)|_(P1a) ≈I _(D)|_(P2a) ≈I _(D)|_(P3a) ≈I _(D)|_(P4a) ≈I _(ra). R _(f1a) =R _(f2a) =R _(fa). The sum of currents at node 4 a and 3 a must equal zero. In other words: I _(D)|_(P2a) +I _(Ria) +I _(Rfa)=0. Also, I _(Rfa)≈(V _(ra) −V _(EB))/R _(fa) I _(ra) =V _(ra) /R _(Oa) I _(ra) +[V _(T).×ln(a×b)]/R _(ia) +I _(Rfa)≈0 Thus, V _(ra) /R _(Oa) +[V _(T)·ln(a×b)]/R _(ia)+(V _(ra) −V _(EB))/R _(fa)≈0 Solving for V_(ra) in the above equation (with b=1), we therefore get: V _(ra) ≈[V _(EB)+(R _(fa) /R _(ia))×V _(T)×ln(a)]×(1+R _(fa) /R _(Oa))⁻¹

The method of operation of the FIG. 1 embodiment may be summarized as follows. An I_(PTAT) or I_(Ria) is generated in the Q_(2a)−R_(ia)−A_(1a)−Q_(1a) voltage loop via ΔV_(EB) of Q_(2a)−Q_(1a) placed across R_(ia), where ΔV_(EB)≈V_(EB)|_(Q1a)−V_(EB)|_(Q2a)≈V_(T)×ln(a×b). Concurrently, the sum of currents at a circuit node (node 4 a) are zero, meaning that I_(Rf2a)+I_(D)|_(P2a)=0. Amplifier A_(2a) accommodates the (unity gain) buffering and the feeding back of V_(ra) on to R_(f1a) and R_(f2a). Hence, I_(Rfa) (V_(ra)−V_(EB))/R_(fa) which increases with temperature since V_(ra) is designed to have near zero TC while V_(EB) voltage decreases with temperature. Therefore, since I_(RF2) which increases with temperature can provide the positive TC I_(Ria), then (in order for A_(1a) to keep its inputs substantially equal) amplifier A_(1a) provides the gates of P_(1a)-P_(4a) (current sources) with a voltage such that P_(1a)-P_(4a) will have near zero TC currents. Thus, I_(D)|_(P2a)≈V_(ra)/R_(Oa) which is I_(ra) and has a near zero TC.

To describe some of the benefits of this embodiment, an example may be helpful. Given that V_(EB) has a −2 mV/° C., let us say V_(EB)|_(T=cold)=0.8V, V_(EB)|_(T=ambient)=0.6V, and V_(EB)|_(T=hot)=0.4V. The circuit is configured such that V_(ra)|_(cold>T>hot)=0.6V. Also note that current consumption of the FIG. 1 circuit embodiment can be in a predetermined range of for example 1 micro ampere to 5 micro amperes, depending on considerations such as die size and power consumption objectives amongst others.

Another benefit is that the current consumption at ambient temperature is minimized, and this is advantageous because some applications operate in ambient most of the time but need to withstand hot and cold temperature hikes sometimes. The current through R_(f1a) and R_(f2a) is nearly zero since the voltages across them are nearly zero: V_(ra)|_(cold>T>hot)=0.6V=V_(EB)|_(T=ambient)=0.6V. Note also that here the zero current crossing point can be set to the middle of hot and cold temperature.

Another benefit of the FIG. 1 embodiment is that the same amplifier A_(2a) may be used to generate I_(ra) and V_(ra). Furthermore, A_(2a) may be configured as a unity gain buffer amplifier which has some current output drive capability and can eliminate the need for an external amplifier for driving some output loads. Besides cost, an external amplifier can contribute to additional offset and gain error variation over temperature.

Conventional bandgaps (such as the one depicted in FIG. 5) as well as this proposed embodiment would require trimming for more precise TC. A trim for TC in the embodiment disclosed in FIG. 1 goes a longer way since both I_(ra) and V_(ra) values (with A_(1a) to provide some voltage output drive capability) can be centered for optimal TC with the same single trim as opposed to multiple trims for each of V_(ra), I_(ra), and one to null-out the non-ideal effects of an external buffer amplifier.

Another advantage of the embodiment of FIG. 1 is that by programming different R_(Oa), R_(fa), or scaling P_(1a)-P_(4a), different fractional bandgap voltages can be attained.

Another benefit of the FIG. 1 embodiment is that it also allows for decoupling of V_(SS) and ground (GND), where technically V_(ss) can run at a lower voltage than the ground potential. Note that V_(DD) may be lowered to substantially similar value by which the V_(ss) is lowered limited by the forward biasing of base-collectors of Q_(1a) and Q_(2a). Such capability of this embodiment can accommodate proper operations of the Bandgap reference at lower V_(DD) while V_(ra) remains referenced to the ground potential.

Supply voltage coefficient and bandgap's TC of this embodiment should also benefit from the circuit in FIG. 1 for at least 2 reasons: (1) there is more temperature stability associated with current sources P_(1a)-P_(4a) which are biased with V_(ra)/R_(Oa) which is a current with near zero TC; and (2) transistors P_(3a)-P_(4a) drain voltages are centered near V_(ra), which at the middle point of P_(1a)-P_(2a) drain voltages that shift around V_(ra) from 400 mV at hot temperatures to 800 mV at cold temperatures. This should minimize and help center systematic mismatch due to V_(A) (early voltage of CMOS transistors) of PMOS transistors, and variations of V_(ra) over V_(DD) and temperature spans.

The embodiment of FIG. 1 further allows for stacking CMOS transistors to help enhance the output impedance of current sources P_(1a)-P_(4a). Note also that V_(ra) can be fed back through only one resistor R_(f1a) to the Q_(1a) side. Eliminating R_(f2a) can save power and area at the expense of additional bow in TC.

In the embodiments disclosed in FIGS. 2 and 3 a bandgap voltage, V_(BG), is generated by adding a PTAT voltage, V_(PTAT), whose voltage increases with temperature (positive TC) to a CTAT voltage, V_(CTAT), whose voltage decrease with temperature (negative TC). Henceforth, summation of the V_(CTAT) (with a negative TC) and V_(CTAT) (with a positive TC) can be scaled via resistors (divider) to produce a fractional bandgap voltage, V_(rb), which is substantially constant over temperature variation. To accomplish this objective in standard CMOS and in the context of low supply voltage and current, alternative embodiments are shown in FIG. 2 and another in FIG. 3. These embodiments include elements such as amplifiers, resistors, BJT, and CMOS transistors that can be configured to function as current sources. The embodiments of FIGS. 2 and 3 improve bandgap's cost-performance by maintaining low current consumption, keeping the bandgap operational at lower power supply, and maintaining stability over frequency while keeping the die size small to keep the cost down.

FIG. 2 is a circuit schematic showing a fractional bandgap reference. The embodiment depicted in FIG. 2 establishes a PTAT current (I_(Rib)) in P_(3b) via forcing a ΔV_(EB) across R_(ib), where ΔV_(EB)=V_(T)×ln(a×b) which is a PTAT signal. Note that Q_(2b) is ‘a’ times the size Q_(1b), and P_(1b) is ‘b’ times the size of P_(2b). Amplifier A_(1b) is configured in unity gain to set the voltage at one side of R_(ib) to V_(EB) of Q_(2b). Conjointly, amplifier A_(2b) substantially equalizes the voltage on the other side of R_(ib) (by providing enough voltage to the gate of P_(3b)) with V_(EB) of Q_(1b). Therefore a voltage of ΔV_(EB)≈V_(EB)|Q_(1b)−V_(EB)|Q_(2b) is generated across R_(ib). The current I_(Rib)=I_(PTAT) is properly scaled and mirrored in P_(1b) through P_(4b), where P_(4b) feeds such scaled I_(PTAT) to the output node at V_(rb). In concert, a CTAT current I_(Rfb) flows through R_(fb), which is generated via the same V_(EB) of Q_(2b), after it is buffered by unity gain amplifier A_(1b). The aggregation of the three currents I_(Rfb), I_(Rib), and I_(Rob) at the output node 7 b generates the desired V_(rb). This embodiment segregates the quiescent currents of Q_(1b)-Q_(2b)-P_(1b)-P_(2b) loops from the currents that flows through R_(ib), R_(fb), and R_(Ob). Such implementation provides a needed flexibility in biasing Q_(1b)-Q_(2b), including operating them at advantageously lower quiescent currents, to minimize the V_(EB) voltage drop (without requiring prohibitively large R_(ib) or R_(fb) or R_(Ob)). This move, in turn can free up the scarce operational supply voltage headroom, especially in deep sub-μ CMOS sub-1V power supply environments, where every 10s of mV counts. For example, lowering the quiescent current in the Q_(1b) and Q_(2b) BJTs from 10 μA to 5 nanoamperes (nA) lowers V_(EB) by about 200 mV, which translates to gaining back about 20% of extra V_(DD) supply headroom in sub-1V environments. By segregating low quiescent currents in Q_(1b) and Q_(2b) BJTs from the PTAT and CTAT signal loop, very large value resistors R_(ib), R_(fb), R_(Ob) may be avoided (e.g. in the 10 MΩ+ range for currents in 10s of nA).

The connections of elements in FIG. 2 are now described. Transistors P_(1b), P_(2b), P_(3b), and P_(4b) have their source terminals connection to node 1 which is the positive supply voltage or V_(DD). Transistors R_(1b) through P_(4b) have their gates connected to node 6 b, whose voltage is set by the output node of amplifier A_(2b). At node 3 b, drain of P_(1b) is connected to the emitter of BJT, Q_(1b), as well as the inverting input terminal of amplifier A_(2b). At node 2 b, drain of P_(2b) is connected with the emitter of BJT, Q_(2b), as well as the non-inverting node of amplifier A_(1b). At node 4 b, drain of P_(3b) is connected to resistor R_(ib) as well as non-inverting input terminal of A_(2b). At node 7 b, which is the output of the reference voltage V_(rb), drain of P_(4b) is connected to resistor R_(ob) as well as resistor R_(fb). The other side of R_(Ob) is connected to ground (GND), which can be at a different voltage that V_(ss) where base and collector terminals of Q_(1b) and Q_(2b) are connected to V_(SS). At node 5 b, R_(ib) is connected to R_(fb), which are connected to the output of A_(1b). Note that at node 5 b, amplifier A_(1b) has its inverting input terminal connected to its output, which configures A_(1b) as a voltage unity gain buffer amplifier, where the voltage at the non-inverting input of A_(1b) is substantially equalized with the voltage its output at node 5 b. Amplifier A_(2b) is utilized here to substantially equalize its negative at node 3 b with its positive input at node 4 b. Setting the source voltages of transistors P_(ib) through P_(4b) to the same voltage at node 1 b (which is V_(DD)) and setting their gates to the same voltage at node 6 b enables configuring transistors R_(1b) through P_(4b) as four current sources whose quiescent currents can be scaled substantially proportional to their respective transistors' width over length ratios, W/L. For example, in the FIG. 2 circuit schematic (W/L)_(P1b)=b×(W/L)_(P2b), and (W/L)_(P3b)=c×(W/L)_(P2b), and (W/L)_(P4b)=d×(W/L)_(P2b), which accommodates scaling P_(1b), P_(3b), and P_(4b) quiescent currents to be substantially scaled as multiples of ‘b’, ‘c’, and ‘d’ times the quiescent current in P_(2b).

The details of various methods of operation of the circuit in FIG. 2 is described in the following segment. We begin by describing the voltage loop that starts (at node 0 which is the V_(SS)) going through Q_(2b) (to node 2 b) then across A_(1b) (to node 5 b) then through R_(ib) (to node 4 b) then across A_(2b) inputs (to node 3 b) and finally through Q_(2b) back to node 0. In this voltage loop, amplifiers A_(1b) and A_(2b) have substantially minimal offset voltages (note that V_(EB) of Q is denoted as V_(EB)|_(Q)) V _(EB)|_(Q1b) ≈I _(PTAT) ×R _(ib) +V _(EB)|_(Q2b), where I _(PTAT) ≈I _(Rib). Thus: V _(EB)|_(Q1b) −V _(EB)|_(Q2b) ≈I _(PTAT) ×R _(ib) ≈ΔV _(EB). Therefore, I _(D)|_(P3b) ≈I _(PTAT) ≈ΔV _(EB) /R _(ib)≈(V _(EB)|_(Q1b) −V _(EB)|_(Q2b))/R _(ib) To generate ΔV_(EB), the emitter areas of Q_(2b) are scaled ‘a’ times bigger than that of Q_(1b), and as described earlier the quiescent currents for Q_(1b) and Q_(2b) can be scaled via P_(2b) and P_(1b) currents, whose W/Ls are scaled by ‘b’: ΔV _(EB) ≈V _(EB)|_(Q1b) −V _(EB)|_(Q2b) ≈V _(T)×ln(a×b). Thus: I _(D)|_(P3b) ≈I _(PTAT) ≈ΔV _(EB) /R _(ib) ‥[V _(T)×ln(a×b)]/R _(ib). Note for example that for a=5 and b=11, then 100 mV≈VT×ln(55) could be a typical value of [V_(T)×ln(a×b)] term in the above equation. Consistent with principles of conventional bandgaps (such as the one depicted in prior art FIG. 5), note that ΔV_(EB) tracks V_(T) which has a positive TC, and this yields the PTAT signal (current) needed in the bandgap.

Next is a summary of what has been described thus far about the FIG. 2 bandgap which pertains mostly to the operation of PTAT signal generation. Amplifier A_(1b) (which is configured in unity gain with its inverting input connected to its output) operates as a buffer for V_(EB)|_(Q2b) voltage to be fed to one side of R_(ib). Concurrently, amplifier A_(2b) senses the V_(EB)|_(Q1b) at its inverting input and while the output of A_(2b) generates the needed gate voltage for P_(3b). Configured as such, transistor P₃ drain current feeds the other side of R_(ib) in order for A_(2b) to substantially equalizes its (inverting and non-inverting) inputs it to V_(EB)|_(Q1b). Hence, the voltage across R_(ib) is set to ΔV_(EB)=V_(EB)|_(Q1b)−V_(EB)|_(Q2b) which is a P_(TAT) current or I_(PTAT). As noted earlier, given that A_(2b) drives the gates P_(1b) through P_(4b), whose sources are all connected the V_(DD), then the quiescent current of P₁ through P₄ are also scaled (by ‘b’, ‘c’, ‘d’) as a function of I_(PTAT), which has a positive temperature coefficient as stated earlier.

The circuit of FIG. 2 enables Q_(1b) and Q_(2b) quiescent currents to be scaled and track I_(PTAT), which has a positive TC. An important benefit of this embodiment is that it also concurrently accommodates both Q_(1b) and Q_(2b) to operate at currents that are segregated (or isolated) from the current through R_(ib). Such segregation results in feasible and meaningful design flexibility to scale the ratio (‘n’) of currents in R_(ib) as compared to the quiescent currents in Q_(1b) and Q_(2b), to accommodate low voltage supply operations, which will be explained shortly. Since the current through R_(i) is I_(PTAT)≈I_(D)|_(P3), then the current through Q_(1b) and Q_(2b) can be I_(PTAT)/n. For example, the amount of I_(PTAT) current through R_(ib) can be typically in the 10 μA level, while because of the segregation, the amount of I_(PTAT) current through BJTs Q_(1b) and Q_(2b) can be scaled down in the 5 nA levels, which make n=10 μA/5 nA=2000. In this example, by lowering quiescent currents of BJTs by 2000, then the V_(EB) in Q_(1b) and Q_(2b) is lowered by V_(T)×ln (2000) which is about 200 mV. Having 100 mV to 200 mV less voltage across V_(EB) in sub-1V power supply environments is about 10% to 20% of extra headroom, which is very beneficial for bandgap operations to specifications with lower power supplies. Also note that current consumption of the FIG. 2 circuit embodiment can be predetermined in the range of for example 0.5 micro ampere to 2 micro amperes, depending on considerations such as die size and power consumption objectives, amongst others.

Moreover, by segregating the Q_(1b) and Q_(2b) currents from R_(ib), the circuit of FIG. 2 has another benefit which allows for small size R_(ib) at very low currents. To make the point more clear a comparison with (such as the one depicted in FIG. 5) bandgaps may be helpful. As in the cases with ordinary bandgaps, R_(ib) is generally in series with emitter of Q_(2b), and in such schemes both R_(ib) and Q_(2b) quiescent currents must be the same or in the μA ranges. To reduce the V_(EB) of Q_(2b), its quiescent current needs to be substantially reduced. For example, if one were to design for ΔV_(EB)=100 mV and 5 nA of quiescent current through both R_(ib) and Q_(2b), then that would require a 20 MΩ resistor which is size prohibitive. Instead, this embodiment allows for ΔV_(EB)=100 mV across R_(ib) with current of 10 μA which makes R_(ib)=10KΩ which is very feasible and economical. In this example, therefore 2000 times smaller resistor and 20% extra headroom for sub-1V power supply environment is achieved. Area and headroom benefits less than 2000 and 20% (respectively) would make using the embodiment in FIG. 2 worth the while.

Now we turn to describing the CTAT and fractional voltage generation of this embodiment. The fractional bandgap voltage or V_(rb) at node 7 b is provided with (1) the PTAT signal, which is via the drain terminal of P_(4b) feeding the equivalent parallel resistors R_(Ob) and R_(fb) and (2) the CTAT signal, which unity gain amplifier A_(1b) feeds the resistor divider of R_(Ob) and R_(fb). The method to arrive at the fractional bandgap voltage is described as follows. The sum of currents at node 7 b must equal zero. In other words, I_(D)|_(P3b)+I_(Rob)+I_(Rfb)=0. Note that I_(D) Of P_(3b) is denoted as I_(D)|_(P3b). Transistor P_(4b) is a current source, whose current is a function of I_(PTAT) with a positive TC. If scale factors c=d then (W/L)_(p3b)=(W/L)_(P4b) causes, I_(D)|_(P3b)=I_(D)|_(P4b). We showed earlier that: I _(D)|_(P4b) ≈I _(D)|_(P3b) ≈I _(PTAT) ≈[V _(T)×ln(a×b)]/R _(ib) Moreover, at node 7 b it can be seen that I_(Rob)=V_(rb)/R_(Ob) and I_(Rf)=(V_(EB)−V_(r))/R_(f). Given that I_(D)|_(P3)+I_(RO)+I_(Rf)=0, therefore the simplified mathematical solution for V_(rb) can be described as: V _(rb) ≈V _(BG)×(1+R _(fb) /R _(ob))⁻¹ ≈(m×V _(T) +V _(EB))×(1+R _(fb) /R _(ob))⁻¹. ≈[(R _(fb) /R _(ib))×V _(T)×ln(a×b)+V _(EB)]×(1+R _(fb) /R _(ob))⁻¹. Note for example that for a=5 and b=11, then 100 mV≈VT×ln(55) could be a typical value of V_(T)×ln(a×b) term in the above equation. Note that in the equation above, V_(EB) generates the CTAT voltage, which is added to that PTAT voltage (m×V_(T)) to generate a V_(BG), where ‘m’ is a constant set by designing the proper scale factors in (a×b) and R_(fb)/R_(ib). Production yields are significantly optimized when specifications depend on constants such as ‘m’ that are derived from ratios of transistor sizes. As just described in this embodiment, manufacturing yields are not compromised here because the V_(BG) and V_(rb) terms depend on ‘a’ which is the ratio of sizes of Q_(1b) and Q_(2b), and “b” which is the ratio of W/L of P_(1b) and P_(2b), and R_(fb)/R_(ib) and R_(fb)/R_(ob) which are the ratios of 2 resistors.

An example to describe the ratio of transistor and resistors sizes for this embodiment is presented. As noted earlier, a typical value of V_(EB) of a particular parasitic BJT device in a CMOS process is +0.6V with TC of −2 mV/° C. The value of V_(T) is about +25.8 mV with TC of +0.086 mV/° C. To generate a voltage that has a near zero TC, ‘m’ needs to be set at a multiple of 23.25, which is derived from ratio of TC of V_(EB) (−2 mV mV/° C.) to TC of V_(T) (+0.086 mV/° C.). Hence, V_(BG)≈m·V_(T)+V_(EB)≈1.2V. Moreover, by choosing R_(fb)=R_(Ob), then a fractional V_(rb) voltage of V_(BG)/2 or 0.6V can be produced, which is desirable in sub-1V power supply applications.

Recall that the PTAT signal is generated while current through R_(ib) is segregated from quiescent current through Q_(2b), in order to keep V_(EB) low and resistor sizes feasible. Similarly, this embodiment enables generating the CTAT signal from the same V_(EB) of Q_(2b) where the quiescent current in Q_(2b) is segregated from the current through R_(fb) via the same amplifier A_(1b) which is configured as a unity gain buffer amplifier. As was the case in the PTAT signal path, here in the CTAT signal path, there is a material benefit in segregating Q_(2b) from R_(fb), where normal currents (e.g. in the μA levels) can run through R_(fb) in order to keep the size of R_(fb) small for optimal die cost, while running current through Q_(2b) very small (e.g. in the nA levels) to keep Q_(2b) V_(EB) low and hence improve power supply headroom for sub-1V application. Note that unity gain amplifier buffer A_(1b) segregates Q_(2b) (which operate at very low currents) from R_(fb) by sinking and sourcing current changes in R_(fb) (as V_(rb) is kept constant while V_(EB) of Q_(1b) decreases with temperature) where R_(fb) currents are ‘n’ times higher that Q_(2b) quiescent currents. As such one of the additional benefits of this embodiment is that the same V_(EB) of Q_(2b) plays a central part in generating the CTAT and PTAT signals which improves manufacturing reliability.

The embodiment of FIG. 2 has an additional benefit which is a more stable frequency response when compared with conventional bandgaps (such as the one depicted in FIG. 5 which require a large size R_(ib) in series with emitter of Q_(2b)). By operating the currents in the nano-ampere level, P_(2b) and P_(1b) operate in subthreshold, where PMOS transistors behave like pseudo-BJTs. Therefore, current sources P_(1b) and P_(2b) (which behave like pseudo BJTs) provide the quiescent currents for BJTs Q_(1b) and Q_(2b). As such, small signal frequency response in P_(2b)-Q_(2b) and P_(1b)-Q_(1b) signal paths would depend on and track V_(T)/I_(BIAS)≈1/g_(m), and will largely not depend on the segregated R_(ib), which would have otherwise interfered with frequency response as is the case with conventional bandgaps (such as the one depicted in FIG. 5). Moreover, because I_(BIAS) of P_(2b)-Q_(2b) and P_(1b)-Q_(1b) transistors are scaled as a multiple of I_(PTAT) with a positive TC, their frequency response would also track to be more stable over temperature variations.

Another benefit of FIG. 2 embodiment is that it also allows for decoupling of V_(SS) and ground (GND), where technically V_(SS) can run at a lower voltage than the ground potential. Note that V_(DD) may be lowered to substantially similar value by which the V_(SS) is lowered limited by the forward biasing of base-collectors of Q_(1b) and Q_(2b). Such capability of this embodiment can accommodate proper operations of the Bandgap reference at lower V_(DD) while V_(rb) remains referenced to the ground potential.

The inclusion of the second amplifier in both FIGS. 2 and 3 will negatively contribute to higher noise and higher offset. Including the offset and noise (simplifying the equation to V_(OFNS)˜V_(OFFSET)+V_(NOISE) as an example) of the amplifiers in the V_(rb) equation can be approximated as follows: V _(rb)≈[(R _(fb) /R _(ib))×V _(T)×(ln(a))+V _(EB)]×(1+R _(fb) /R _(ib))⁻¹+[(R _(fb) /R _(ib))×(V _(OFNS1) ±V _(OFNS2))−V _(OFNS2)]×(1+R _(fb) /R _(ob))⁻¹. However, this impact on noise and offset is minimal and manageable by the embodiment of FIG. 2. Firstly, although Q_(1b) and Q_(2b) BJT's noise contribution increases with lowered currents, noise is generally dominated by the CMOS section (amplifiers and current sources) and not the BJTs. Secondly, the multi-billion dollar annual investments in the manufacturing of CMOS fabrication processes, over the last few decades, has significantly improved devise matching, noise, and offset performance which will also benefit this embodiment. Thirdly, the manufacturing yield impact due to the second amplifier offset is minimal. This is explained as follows. For demonstrative simplicity let us assume that identical amplifiers A_(1b) and A_(2b) have similar V_(offset), and that b=c=1 and R_(ob)=R_(fb). Statistically, the contribution of amplifiers A₁ b and A_(2b) random inaccuracies (non-systematic and random offset voltage, noise, and drift) in the PTAT loop (Q_(1b)-A_(1b)-R_(ib)-A_(2b)-Q_(1b)) follow the square root of sum of squares of such random effects. As such, employing an extra amplifier, A₁ b, should not statistically translate to doubling the impact of amplifier's noise and offset on the V_(rb) output. That is the statistical contribution of amplifier offset voltage (V_(ofs)) could approximately be as follows: [√2(R _(fb) /R _(ib))−1]×V _(ofs).

FIG. 3 is a circuit schematic showing a third embodiment which is an alternative bandgap reference to FIG. 2. Here, the voltage loop consisting of R_(ic), Q_(2c), A_(1c), and Q_(1c) forces a difference V_(EB), or ΔV_(EB), voltage to be placed across R_(ic). The current ΔV_(EB)/R_(ic) is the I_(PTAT) current that is mirrored via P_(3c) onto P_(1c), P_(2c) and P_(4c). Concurrently, V_(EB) of Q_(2c) feeds R_(fc), which constitutes the CTAT signal. Similarly, note that Q_(2c) is ‘a’ times the size of Q_(1c) and P_(1c) is ‘b’ times the size of P_(2c). In FIG. 3, the PTAT signal through P_(4c) and CTAT signal through R_(fc) are then summed and scaled at the V_(rc) node, by the ratio of R_(fc) and R_(Oc) to generate the desired fractional V_(BG). With R_(ic) connected to base of Q_(2c) to ground, the PTAT current through R_(ic) (e.g. in the μA level) is segregated from the quiescent current in the Q_(1c) and Q_(2c) BJTs (e.g. in the nA level). Running currents in R_(ic), R_(fc), R_(Oc) at normal currents allows for small size resistors which save die costs, while concurrently running Q_(1c) and Q_(2c) at very low currents reduces V_(EB) voltage of Q_(1c) and Q_(2c) which helps operating the fractional bandgap at lower power supply voltage.

The connections of elements in FIG. 3 will now be described. Given the commonalties between embodiments of FIG. 2 and FIG. 3, descriptions of circuit operations and benefits that overlap between them and that have been covered in the section for FIG. 2 are not discussed in detail. Transistors P_(1c), P_(2c), P_(3c), and P_(4c) have their source terminals connection to node 1 which is the positive supply voltage or V_(DD). Transistors P_(1c) through P_(4c) have their gates connected to node 6 c, whose voltage is set by the output node of amplifier A_(2c). At node 3 c, drain of P_(1c) is connected to the emitter of BJT, Q_(1c), as well as the inverting input terminal of amplifier A_(2c). At node 2 c, drain of P_(2c) is connected with the emitter of BJT, Q_(2c), as well as the non-inverting node of amplifier A_(1c) plus the non-inverting node of amplifier A_(2c). At node 4 c, drain of P_(3c) is connected to resistor R_(1c) as well as the base terminal of BJT transistor Q_(2c). At node 7 c, which is the output of the reference voltage V_(rc), drain of P_(4c) is connected to resistor R_(Oc) as well as resistor R_(fc). The other side of R_(Oc) is connected to ground (GND), which can be at a different voltage than V_(SS) when base and collector terminals of Q_(1c) and Q_(2c) are connected to V_(SS). At node 5 c, R_(fc) is connected to the output of amplifier A_(1c) which is configured in unity gain (functioning as a voltage buffer) with its inverting input connected to its output. Amplifier, A_(2c) is utilized here to substantially equalize its negative at node 3 c with its positive input at node 4 c. Setting the source voltages of transistors P_(1c) through P_(4c) to the same V_(DD) voltage at node 1 c and setting their gates to the same voltage at node 6 c enables configuring transistors P_(1c) through P_(4c) as four current sources. Here, P_(1c)-P_(4c) quiescent currents can be scaled substantially proportional to their respective transistors' width over length ratios, W/L. For example, in the FIG. 3 circuit schematic (W/L)_(P1c)=b×(W/L)_(P2c), and (W/L)_(P3c)=c×(W/L)_(P2c), and (W/L)_(P4c)=d×(W/L)_(P2c), which accommodates scaling P_(1c), P_(3c), and P_(4c) quiescent currents to be substantially scaled by ‘b’, ‘c’, and ‘d’ times the quiescent current in P_(2c).

The details of various methods of operation of the circuit in FIG. 3 is described in the following segment. We begin by describing the voltage loop that starts (at node 0) going through R_(ic) (to node 4 c) then over Q_(2c) (to node 2 c) then across A_(2c) (to node 3 c) then across Q_(2c) back to node 0. To describe operation of this voltage loop, amplifiers A_(1c) and A_(2c) will have substantially minimal offset voltages: I _(PTAT) ×R _(ic) V _(EB)|_(Q2c) ≈V _(EB)|_(Q1c), where I _(PTAT) ≈I _(Ric). Thus: V _(EB)|_(Q1c) −V _(EB)|_(Q2c) ≈I _(PTAT)×_(Ric) ≈ΔV _(EB). Therefore, I _(D)|_(P3c) ≈I _(PTAT) ≈ΔV _(EB) /R _(ic)≈(V _(EB)|_(Q1c) −V _(EB)|_(Q2c))/R _(ic) ΔV _(EB) ≈V _(EB)|_(Q1c) −V _(EB)|_(Q2c) ≈V _(T)×ln(a×b). Hence: I _(D)|_(P3c) ≈I _(PTAT) ≈ΔV _(EB) /R _(ic) ≈[V _(T)×ln(a×b)]/R _(ic).

Note for example that for a=5 and b=11, then 100 mV≈VT×ln(55) could be a typical value of [V_(T)×ln(a×b)] term in the above equation. Let us summarize what has been described thus far about embodiment of the FIG. 3 bandgap, which pertains mostly to the operation of PTAT signal generation. Amplifier A_(2c) substantially equalizes its inputs, which are connected to emitters of Q_(1c) and Q_(2c), by way of A_(2c)'s output driving P_(3c)'s gate. Transistor P_(3c), configured as such, provides enough current via its drain terminal to the top of R_(ic) which produces a voltage at node 4 c that is equal to the difference voltage between V_(EB) of Q_(1c) and V_(EB) of Q_(2c). In summary, the voltage across R_(ic) is set to ΔV_(EB)=V_(EB)|V_(EB)|_(Q2c) which is a P_(TAT) current or I_(PTAT). As noted earlier, given that A_(2c) drives the gates P_(1c) through P_(4c), whose sources are all connected the V_(DD), then the quiescent current of P_(1c) through P_(4c) are also scaled (by ‘b’, ‘c’, ‘d’) as a function of I_(PTAT), which has a positive temperature coefficient as stated earlier.

As was the case with the embodiment in FIG. 2, the embodiment in FIG. 3 has the important benefit of segregating Q_(1c) and Q_(2c) to operate at very low currents compared to the current that flows through R_(ic). Since current through R_(ic) is I_(PTAT)≈I_(D)|_(P3c), then the current through Q_(1c) and Q_(2c) can be I_(PTAT)/n. By lowering quiescent of BJTs by ‘n’, then the V_(EB) in Q_(1c) and Q_(2c) is lowered by V_(T)×ln(n), which can be in the range of 150 mV to 200 mV. Having 150 mV to 200 mV less voltage across V_(EB) in sub-1V power supply environments is about 15%-20% of extra headroom, which is very beneficial for bandgap operations to specifications with lower power supplies. Also note that current consumption of the FIG. 3 circuit embodiment may be a predetermined value for example in the range of 500 nano amperes to 2 micro amperes, depending on considerations such as die size and power consumption objectives amongst others.

Note that in this embodiment, the error due to BJT's low β (e.g. in the 1-5 range) is attenuated by ‘n’ or I_(Ric)/I_(Q2c) ratio, where I_(Ric) is the current through R_(ic) (the PTAT resistor), and I_(Q2c) is the quiescent current through Q_(2c) BJT.

Similar to the operational principles of FIG. 2, in the embodiment of FIG. 3, by segregating the Q_(1c) and Q_(2c) currents from R_(ic), another benefit is realized which is keeping size of R_(ic) small despite Q_(1c) and Q_(2c) very low currents.

Now we turn to describing the CTAT and fractional voltage generation of this embodiment. Amplifier A₁ c, configured as a unity gain buffer amplifier functions to segregate V_(EB) of Q_(2c) which operates in nano-ampere current levels (a CTAT signal) and A_(1c) functioning as a buffer to absorb the sink and source currents through R_(fc) which operates with micro ampere levels. As stated earlier, this is beneficial because the same V_(EB) of Q_(1c) is used to generate CTAT and PTAT signals, V_(EB) of Q_(1c) is kept low to help operations at lower V_(DD), and keep resistor R_(fc) size small by running normal current levels through it.

The method to arrive at the fractional bandgap voltage is described as follows. The sum of currents at node 7 c must equal zero. For c=d we get I_(D)|_(P3c)=I_(D)|_(P4c).

Moreover, at node 7 c it can be seen that I_(ROc)=V_(rc)/R_(Oc) and I_(Rfc)=(V_(EB)−V_(rc))/R_(fc). Similar to the principle of operations in FIG. 2, for the embodiment in FIG. 3 we also have I_(D)|_(P3c)+I_(ROc)+I_(Rfc)=0, therefore the simplified mathematical solution for V_(rc) can be described as: V _(rc) ≈V _(BG)×(1+R _(fc) /R _(oc))⁻¹ ≈(m×V _(T) +V _(EB))×(1+R _(fc) /R _(oc))⁻¹ ≈[(R _(fc) /R _(ic))×V _(T)×ln(a×b)+V _(EB)]×(1+R _(fc) /R _(oc))⁻¹.

As previously discussed, to get optimal manufacturing fabrication yields, it is best to have performance specification depend on geometric ratios of devices available in the fabrication process. Here also, manufacturing yields are not compromised because the V_(BG) and V_(rc) terms depend on ‘a’ which is the ratio of sizes of Q_(1c) and Q_(2c), and “b” which is the ratio of W/L of P_(1c) and P_(2c), and R_(fc)/R_(ic) and R_(fc)/R_(oc) which are resistor ratios.

Similarly to FIG. 2, the embodiment of FIG. 3 has an additional benefit which is a more stable frequency response, when compared with conventional bandgaps (such as the one depicted in FIG. 5 which require a large size R_(ic) in series with emitter of Q_(2c)). Also, a similar benefit of FIG. 3 embodiment is that it also allows for decoupling of V_(SS) and ground (GND), where technically V_(SS) can run at a lower voltage than the ground potential. Note that V_(DD) may be lowered to substantially similar value by which the V_(SS) is lowered limited by the forward biasing of base-collectors of Q_(1c) and Q_(2c). Such capability of this embodiment can accommodate proper operations of the Bandgap reference at lower V_(DD) while V_(rb) remains referenced to the ground potential.

For similar reasons discussed earlier, contribution in noise and offset due to lower currents and the extra amplifier are mitigated when compared to conventional bandgaps (such as the one depicted in FIG. 5).

As noted earlier, the risk and error due to BJT's low β (e.g. in the 1-5 range) is attenuated by ‘n’ or I_(Ric)/I_(Q2c) ratio. However, in certain CMOS fabrication processes where the base leakage current of parasitic BJTs (Q_(2c) which connected to R_(ic)) can derail high temperature accuracy. For such fabrication cases, the embodiment of FIG. 2 may be a more rugged solution.

The embodiment disclosed in FIG. 4 enables ultra low currents while preserving optimal performance, manufacturing quality, and low costs. Operating at ultra low currents generally requires large size resistors, which can occupy large die areas and thus cost more. Generally, BJT based references that generate a bandgap voltage yield more quality performance, and typically CMOS (non-BJT, non-bandgap) based references that yield ultra-low currents are resistorless. Hence, making large size bandgaps with high value resistors (as in FIG. 5) that have reasonable quality, or making resistorless references (that are not bandgap-based) that may have sub-par quality are two of the conventional approaches to realize ultra low power references. In FIG. 4 note that the circuit diagram consists of elements such as amplifiers, resistors, BJT, and CMOS transistors (i.e. PMOS transistors can be configured to operate as current sources).

The embodiment in FIG. 4 is ultra low power and it is different, among other things, in that it does not use resistors and is bandgap based. A summary of the description on FIG. 4 embodiment is first provided. Parasitic BJTs (such as Q₁ and Q_(d1)) are used to generate a multiple of a thermal voltage, which is V_(T) ln(n×m)=ΔV_(EB)=(such as V_(EB)|_(Q1)−V_(EB)|Q₂). Such multiple of V_(T) is then duplicated in series a proper number of times to generate a PTAT voltage and then added in with a V_(EB) (or CTAT voltage) to produce a 1.25v bandgap voltage. Cascading scaled parasitic BJT V_(EB) followers looped-in with CMOS amplifiers (that have no built in offset), depicted in the embodiment in FIG. 4 offers some advantages. For example, it helps keep current consumption ultra-low and parasitic leakages minimized which can extend the higher temperature span of operation. Operating headroom is maximized in part because of lowered V_(EB) and V_(GS) of CMOS and BJT transistor, which operate in nano-ampere currents levels. Importantly, this embodiment eliminates use of resistors without the need for any special device or process. Such a bandgap can operate at ultra-low currents (i.e. nano-amperes) without using (large size) resistors and without compromising frequency response stability which saves significant die area and improves frequency response in ultra-low currents. This embodiment may be implemented only using standard CMOS processes and may not require any custom or special devices and hence lowers manufacturing cost. Also, importantly, manufacturing yields should improve with this embodiment because statistical (random) contributions from CMOS amplifier noise, offset, and drift terms are not multiplied but accumulated by the square root of sum of the squares, fundamentally because the proposed topology uses summation and not multiplication to generate the bandgap's PTAT term.

FIG. 4 is a circuit schematic showing a bandgap reference according to another embodiment of this invention. Let us start by describing the connections of elements in FIG. 4 with the PTAT signal generation section first. Transistor P_(i), biased at current ‘i’, has its gate and drain connected to node 2 d, which biases equal sized PMOS transistors P₁, P₂, P₃, P₄, P₅, and P₆ to also be biased at current ‘i’. Current source PMOS transistors P₁ through P₆ have their sources connected to node 1, which is V_(DD), and have their drains connected to nodes 6 d, 9 d, 12 d, 15 d, 18 d, and 21 d respectively, which feeds the emitter of nX BJT PNPs in each of V_(T) cell. Specifically, collectors of BJTs Q_(d1), Q_(d2), Q_(d3), Q_(d4), Q_(d5), and Q_(d6) are connected to V_(SS) and their emitters are connected to nodes 6 d, 9 d, 12 d, 15 d, 18 d, and 21 d respectively, which bias the emitter currents of each of nX BJT PNP to about ‘i’. Similarly, transistor P_(m), biased at current ‘m×i’ has its gate and drain connected to node 3 d, which biases equal sized PMOS transistors P_(d1), P_(d2), P_(d3), P_(d4), P_(d5), and P_(d6) to also be biased at current ‘m×i’. Current source PMOS transistors P_(d1) through P_(d6) have their sources also connected to node 1, which is V_(DD), and have their drains connected to nodes 5 d, 8 d, 11 d, 14 d, 17 d, and 20 d respectively, which feeds the other BJT emitter of 1X PNPs in each of V_(T) cell. Collectors of BJTs Q₁, Q₂, Q₃, Q₄, Q₅, and Q₆ are connected to V_(SS), while their emitters are connected to nodes 5 d, 8 d, 11 d, 14 d, 17 d, and 20 d respectively, which biases the emitter currents of each of the 1×BJT PNP to about ‘m×i’. Amplifiers A_(d1), A_(d2), A_(d3), A_(d4), A_(d5), and A_(d6) have their non-inverting inputs connected to nodes 5 d, 8 d, 11 d, 14 d, 17 d, and 20 d respectively, and have their inverting nodes connected to nodes 6 d, 9 d, 12 d, 15 d, 18 d, and 21 d respectively. The output nodes of amplifiers A_(d1), A_(d2), A_(d3), A_(d4), A_(d5), and A_(d6) are connected to nodes 7 d, 10 d, 13 d, 16 d, 19 d, and 22 d respectively. While the base of Q₁ is connected to ground (GND); bases of Q_(d1) and Q₂ are connected to node 7 d; bases of Q_(d2) and Q₃ are connected to node 10 d; bases of Q_(d3) and Q₄ are connected to node 13 d; bases of Q_(d4) and Q₅ are connected to node 16 d; bases of Q_(d5) and Q₆ are connected to node 19 d; and finally bases of Q_(d6) and Q₇ are connected to node 22 d.

A ‘V_(T) cell’ is comprised of current source transistors P_(d1) and P₁ which bias emitters of Q₁ and Q_(d1), respectively, while amplifier A_(d1) generates a voltage at node 7 d such that its inputs at nodes 5 d and 6 d are substantially equalized. Because Q_(d1) is ‘n’ times larger in emitter size than that of Q₁ and because Q₁ is biased at ‘m’ times higher current than Q_(d1), then the difference between V_(BE)s of Q₁ and Q_(d1) is ΔV_(BE)=V_(T) ln(n×m). This ΔV_(BE) is the multiple of thermal voltage, V_(T), that ‘V_(T) cell’ number 1 generates at node 7 d. Therefore, V_(T) cell 1 is made up of transistors P_(d1) and P₁ and amplifier A_(d1); V_(T) cell 2 is made up of transistors P_(d2) and P₂ and amplifier A_(d2); V_(T) cell 3 is made up of transistors P_(d3) and P₃ and amplifier A_(d3); V_(T) cell 4 is made up of transistors P_(d4) and P₄ and amplifier A_(d4); V_(T) cell 5 is made up of transistors P_(d5) and P₅ and amplifier A_(d5); and V_(T) cell 6 is made up of transistors P_(d6) and P₆ and amplifier A_(d6).

V_(T) cells number 1 to 6 each generate a ΔV_(BE)=V_(T) In (n×m), which are configured in a series cascade that yields 6×V_(T) ln(n×m), which is the PTAT voltage. Note for example that for n=5 and m=11, then 100 mV≈VT×ln(55) could be a typical VT cell output voltage. Moreover, note that number of V_(T) cells may be in the range of 5 to 8 depending on ‘L’, ‘m’, and ‘n’ scale factors that can be optimized for current consumption and area objectives on the bandgap.

The CTAT signal generation is simple and generated by Q₇. Transistor P_(L), biased at current ‘L×i’ has its gate and drain connected to node 4 d, which biases equal sized PMOS transistor P₇. This transistor's drain terminal at node 24 d supplies the bias current for emitter of Q₇ that has it collector connected to V_(SS). BJT Q₇ generates the V_(EB) which is the CTAT voltage.

Next is a summary of the description of the FIG. 4 embodiment and a discussion of the impact of non-ideal terms such as CMOS amplifier offset voltages. The proposed V_(T) cell approach depicted in FIG. 4 entails generating a PTAT voltage through 2 parasitic vertical PNP pairs looped by a small CMOS amplifier that operates in subthreshold which constitute ‘V_(T) Cells’. Cascading multiples (i.e., G) stages of such ‘V_(T) cells’ generates the V_(pTAT) (without utilizing resistors), which is added to a V_(EB) at the last (or first) stage to produce the bandgap voltage, V_(BG).

It is commonly known that non-ideal terms of CMOS amplifiers, such as V_(OFS), dominate as compared to BJT non-ideal terms such as that of V_(EB) follower pairs. Hence, V_(BG) is can be approximated as follows: V _(rd) ≈V _(BG) ≈V _(EB) +V _(OFS-total) +G×[V _(T)×ln(n×m)] V _(OFS-total)≈(±V _(OFSd1) ±V _(OFSd2) ± . . . ±V _(OFSdG)). The random statistical contribution of the CMOS V_(oFs) summed in series along within the V_(T) cell can be approximated as: V _(OFS-total)≈[(±V _(OFSd1))²+(±V _(OFSd2))²+ . . . +(±V _(OFSdG))²]^(1/2). Given that CMOS amplifiers are geometrically identical and may be situated next to each other on the same die, the statistical variations of V_(OFSd1) through V_(OFSdG) should fall within a similar statistical band, let's say V_(OFS). As such the statistical contribution of CMOS amplifier V_(OFS) to the final bandgap voltage may be approximated as: V _(OFS-total)≈√(G×V _(OFS) ²)≈V _(OFS) ×√G V _(rd) ≈V _(BG) ≈V _(EB) +V _(OFS) ×√G+G×[V _(T)×ln(n×m)]. CMOS amplifier V_(OFS) in subthreshold (which is where all CMOS transistors of FIG. 4 are under) approximates V_(T) like variations (thus tracking the VT ln [m×n] term by first order approximation), which can be corrected as part of the V_(PTAT) wafer level trim (trim considerations will be described shortly). For comparison sake, it is of note that in conventional bandgaps (such as the ones in prior art FIG. 5) random statistical contribution of non idealities of CMOS amplifier A_(1e), including V_(OFSe1), is amplified by G+1(G=R_(fe)/R_(ie)) instead of √G: V _(rd) ≈V _(BG) ≈V _(EB) +G×(1+R _(fe) /R _(ie))[V _(OFSe1) +V _(T)×ln(n×m)] Therefore the embodiment of FIG. 4 (for a gain of, for example, 6), from a die yield perspective, the V_(OFS) statistical contribution should be 2.4 times (or 6/≈6) less than a conventional bandgap of FIG. 5 (for a gain of 6). Note that the benefit of the embodiment in FIG. 4 should extend in lieu of the same mathematics being applicable to other random non-ideal terms of CMOS amplifier such noise and drift. Another operational benefit of FIG. 4 embodiment should be higher temperature spans. CMOS amplifier input noise and offset voltage is generally lower with larger W/L of especially input transistors. However, because the statistical contribution of CMOS amplifier offset voltage in FIG. 4 is attenuated by √G, then CMOS transistors can be designed with smaller W/L and (as importantly) equally sized transistors inside each V_(T) cell to improve high-temperature performance. Hence, small and (as importantly) equally sized CMOS transistors inside each V_(T) cell amplifier maximize the bandgap's operating temperature span via balancing smaller (transistor) junction areas but large enough for reasonable matching which could contain the derailing impact of leakage currents particularly at high temperatures. Another benefit of the FIG. 4 embodiment is that BJTs and small CMOS amplifiers operate in subthreshold (low V_(EB) and V_(Gs)) so as to optimize bandgaps operating headroom.

Here is more specific descriptions pertaining to the advantages of the resistor-less bandgap of FIG. 4. Standard CMOS process offers gate-poly resistors with resistivity typically in the tens of Ω/square (□) (Ω is the symbol for resistivity and □ denotes unit area). For example, 700 mV (of V_(PTAT) voltage) for every 100 nA of current flow (translate to a 7 MΩ resistor) which is area prohibitive with gate-poly resistivity in the tens of Ω/□. There are second layer poly (i.e. salicided and un-salicided) that offer resistance in the hundreds to thousands Ω/□, but they require extra manufacturing process steps that increase die cost, and also they are less accurate compared to first gate-poly. Also note that current consumption of FIG. 4 circuit embodiment may be a predetermined value for example in the range of 100 nano amperes to 500 nano amperes, depending on considerations such as die size and power consumption objectives amongst others.

Another important benefit of the embodiment of FIG. 4 being resistor-less, is better frequency response stability when compared with conventional CMOS bandgaps or variations such as FIG. 5. Frequency response of the loop containing A_(1e) in conjunction with P_(1e) and P_(2e) can be made stable, but it is inherently challenged because, in the A_(1e), P_(1e), P_(2e) signal loop, P_(1e) and P_(2e) small signals (from node 6 e to nodes 4 e and 3 e) are both inverted and fed back to the inverting and non-inverting node of A_(1e). When bias currents are ultra-low and R_(ie) extra-large (i.e. by making a low current bandgap by utilizing the extra mask with higher resistivity poly, which is in the thousands of Ω/□), the frequency response stability of a FIG. 5 type configuration becomes even more challenging to mange for stability. The embodiment of FIG. 4 is inherently more stable, even in ultra-low currents, because it uses no resistors and it has no such A_(1e), P_(1e), P_(2e) loop.

The embodiment of FIG. 4 can offer quality and performance advantages of BJT based bandgaps, it can also have an approximate die area that is in the ball park of other resistor-less references, fabricated in typical sub-micron CMOS processes, as indicated in the referred literature. As noted earlier, small W/L and ultra-low currents of amplifiers transistors have unfavorable noise impact on the bandgap. However, just one bigger compensation capacitor (C_(C), which can be made by a CMOS transistor with its source and drain shorted) may be used in the last stage of the amplifier chain to further low-pass filter out the noise.

Bandgap references are fundamental building blocks that are used almost in every electronic device. The embodiments disclosed in FIGS. 1-4 of this application may be used in personal computers, cell phones, consumer electronic, audio, automotive, test, imaging, video, defense, and medical electronics. These are some of the systems (but not limited to) that generally use bandgap references. The embodiments disclosed in FIGS. 1-4 may be used as a stand alone function (chip), part of a SOC (system-on-a chip), part of a hybrid (multi-chip), or in an electronic system such as a cell-phone. The embodiments disclosed in FIGS. 1-4 may also be used in applications such as power-on-a-chip (PoC), battery-less & wireless, and Internet-of-things (IoT) which are emerging applications that require very low voltage, very low current, high performance, and low costs (obtainable in standard CMOS fabrication processes).

As described above in the embodiment of FIG. 1 and method thereof, an output voltage (V_(ra)) and V_(BE) are used to generate and feedback a current that supplies a needed positive temperature coefficient (TC) current to the bandgap's PTAT current loop. Such positive TC feedback current facilitates generating the residual near zero TC current which is concurrently fed-forward to an output resistor (R_(OA)) to produce the voltage reference (V_(ra)).

As described above in the embodiment of FIGS. 2 and 3 and methods thereof, by segregating and scaling currents (by n-times) in the BJTs from resistors in a bandgap voltage reference, area is saved and operating current minimized. Scarce power supply head room in sub-1V applications is freed-up in the PTAT loop from V_(EB) by VT×ln (n).

As described above in the embodiment of FIG. 4 and method thereof, without use of resistors, bandgap voltage is generated by adding V_(EB) to a PTAT voltage (G×V_(T)), where G V_(T) is produced by cascading pairs of scaled V_(EB) differential followers (with a built-in offset voltage which is a function of V_(T)) looped-in with small CMOS amplifiers (that have no built in offset) for ultra low currents that keeps parasitic leakage current contained, optimizes operating supply and temperature spans.

In summary, bandgap families disclosed in this application enable the bandgap's operations with (combination levels of) ultra-low power and low supply voltage and with the capacity to deliver optimal temperature and power supply spans. 

The invention claimed is:
 1. A scaled bandgap reference circuit comprising: a proportional to absolute temperature (PTAT) voltage loop having a first transistor, a first amplifier, a second transistor and a first resistor (R_(PTAT)); wherein an output of the first amplifier drives at least two voltage controlled current sources (V_(CCS)) that carry near zero temperature coefficient (TC) scaled bandgap reference currents (I_(SR)) that also provide residual currents for the first transistor, the first resistor, and the second transistor; a second resistor, whose current is provided by at least one of the at least two V_(CCS)'s that carries I_(SR), to generate a near zero TC scaled bandgap reference voltage (V_(sR)); and a feedback loop having a second amplifier that buffers V_(SR), and whose output is fed back to the PTAT voltage loop by a third feedback resistor and a fourth feedback resistor which are connected to inputs of the first amplifier and wherein the third and fourth feedback resistors also provide additional residual currents for the first transistor, the first resistor, and the second transistor.
 2. A scaled bandgap reference circuit comprising: a proportional to absolute temperature (PTAT) voltage loop having a first transistor, a first amplifier, a second transistor, a second amplifier having a plurality of inputs, and a first resistor (R_(PTAT)) having a first terminal and a second terminal; wherein the first amplifier buffers a base-emitter voltage (V_(BE)) of the second transistor, and an output of the first amplifier drives a first terminal of the first resistor to isolate the first resistor from the first and second transistors in the PTAT voltage loop; wherein the plurality of inputs of the second amplifier are connected to the V_(BE) of the first transistor and the second terminal of the first resistor and an output of the second amplifier drives at least three voltage controlled current sources (V_(CCS)) that provide a positive temperature coefficient (TC) current for the first transistor, the second transistor, and the second terminal of the first resistor; a feedback loop having a second resistor and a third resistor, where a first terminal of the second resistor is connected to ground and a first terminal of the third resistor is coupled with the output of the first amplifier; and wherein a near zero TC scaled bandgap voltage reference (V_(SR)) is generated at a second terminal of the second resistor and a second terminal of the third resistor that are coupled together and receive their currents from one of the least three V_(CCS)'s that carry a positive TC current.
 3. A bandgap reference circuit comprising: a plurality of thermal voltage (VT) cells connected in series to produce a proportional to absolute temperature (V_(PTAT)); wherein each of said VT cells comprise an amplifier and scaled transistors operating at scaled currents which are biased by at least two scaled VT cell current sources; said amplifier generating a positive TC output voltage at a base of one of the scaled transistors where the amplifier inputs are substantially equalized; a base emitter voltage (V_(EB)) transistor biased by a current source to generate a complementary to absolute temperature voltage (V_(CTAT)); and wherein the V_(PTAT) and V_(CTAT) are connected in series to create a bandgap voltage reference (V_(BG)).
 4. A method comprising: providing a positive and negative power supply voltage to a thermal voltage (VT) circuit loop composed of at least two transistors that generate a voltage with positive temperature coefficient (TC); and generating a proportional to absolute temperature (PTAT) voltage (V_(PTAT)) by summing a plurality of VT's by cascading several VT circuit loops. 